Possible mechanisms for glacial earthquakes

The large glacial earthquakes reported on by Ekström et al. (2003, 2006) and Tsai and Ekström (2007) have previously been evaluated in terms of their seismic characteristics. In this paper we attempt to take constraints such as known glacial ice properties, outlet glacier size, calving style, and meltwater variability to construct a self-consistent physical model of the glacial earthquake process. Since many glaciological parameters are poorly constrained, we parameterize a number of important processes and estimate a wide range of possible values for some properties. The range of model outputs is thus fairly large, but it is still difficult to match observational constraints under most conditions. We find that only a small class of models is able to satisfy the major observational constraints. These models are characterized by (1) lost basal resistance coupled to viscoelastic deformation with extensive internal crevassing or with low effective elastic modulus and possibly low effective viscosity or (2) by nonequilibrium calving, such as having large icebergs capsize into the glacier front. Although observational constraints cannot definitively rule out any of the proposed classes of mechanisms, the calving model has much stronger support. Fortunately, the various models make different predictions regarding observables that can potentially be measured in the near future

Enhanced continuum damage modeling of mechanical failure in ice and rocks

Modeling fracture in geomaterials is essential to the understanding of many physical phenomenon which may posses natural hazards e.g. landslides, faults and iceberg calving or man-made processes e.g. hydraulic fracture and excavations. Continuum Damage Mechanics (CDM) models the crack as a solid region with a degraded stiffness. This continuum definition of cracks in CDM allows more feasible coupling with other forms of material non-linearity and eliminates the need to track complicated crack geometry. Using CDM to analyze fracture for the modeling of fracture in geomaterials encounters several challenges e.g.: 1) the need to model the multiple physical processes occurring in geomaterials, typically: coupled fluid flow and solid deformation, 2) the need to consider non-local damage and transport in order to capture the underlying long range interactions and achieve mesh-independent finite element solutions and 3) the elevated computational cost associated with non-linear mixed finite element formulations. The research presented in this thesis aims at improving the CDM formulations for modeling fracture geomaterials. This research can be divided into three main parts. The first is the introduction of a novel non-local damage transport formulation for modeling fracture in poroelastic media. The mathematical basis of the formulation are derived from thermodynamic equilibrium that considers non-local processes and homogenization principles. The non-local damage transport model leads to two additional regularization equations, one for non-local damage and the other for non-local transport which is reduced to non-local permeability. We consider two options for the implementation of the derived non-local transport damage model. The first option is the four-field formulation which extends the (u/P) formulation widely used in poroelasticity to include the non-local damage and transport phenomena. The second option is the three-field formulation, which is based on the coupling of the regularization equations under the assumptions of similar damage and permeability length scales and similar driving local stress/strain for the evolution of the damage and permeability. The three-field formulation is computationally cheaper but it degrades the physical modeling capabilities of the model. For each of these formulations, a non-linear mixed-finite element solution is developed and the Jacobian matrix is derived analytically. The developed formulations are used in the analysis of hydraulic fracture and consolidation examples. In the second part, a novel approach for CDM modeling of hydraulic fracture of glaciers is pretended. The presence of water-filled crevasses is known to increase the penetration depth of crevasses and this has been hypothesized to play an important role controlling iceberg calving rate. Here, we develop a continuum damage-based poro-mechanics formulation that enables the simulation of water-filled basal and/or surface crevasse propagation. The formulation incorporates a scalar isotropic damage variable into a Maxwell-type viscoelastic constitutive model for glacial ice and the effect of the water pressure on fracture propagation using the concept of effective solid stress. We illustrate the model by simulating quasi-static hydro-fracture in idealized rectangular slabs of ice in contact with the ocean. Our results indicate that water-filled basal crevasses only propagate when the water pressure is sufficiently large and that the interaction between simultaneously propagating water-filled surface and basal crevasses can have a mutually positive influence leading to deeper crevasse propagation which can critically affect glacial stability. In the third part, we propose a coupled Boundary Element Method (BEM) and Finite Element Method (FEM) for modeling localized damage growth in structures. BEM offers the flexibility of modeling large domains efficiently while the nonlinear damage growth is accurately accounted by a local FEM mesh. An integral-type nonlocal continuum damage mechanics with adapting FEM mesh is used to model multiple damage zones and follow their propagation in the structure. Strong form coupling, BEM hosted, is achieved using Lagrange multipliers. Since the non-linearity is isolated in the FEM part of the system of equations, the system size is reduced using Schur complement approach, then, the solution is obtained by a monolithic Newton method that is used to solve both domains simultaneously. The method is applied to multiple fractures growth benchmark problems and shows good agreement with the literature

Simulating the roles of crevasse routing of surface water and basal friction on the surge evolution of Basin 3, Austfonna ice cap

The marine-terminating outlet in Basin 3, Austfonna ice cap, has been accelerating since the mid-1990s. Stepwise multi-annual acceleration associated with seasonal summer speed-up events was observed before the outlet entered the basin-wide surge in autumn 2012. We used multiple numerical models to explore hydrologic activation mechanisms for the surge behaviour. A continuum ice dynamic model was used to invert basal friction coefficient distributions using the control method and observed surface velocity data between April 2012 and July 2014. This has provided input to a discrete element model capable of simulating individual crevasses, with the aim of finding locations where meltwater entered the glacier during the summer and reached the bed. The possible flow paths of surface meltwater reaching the glacier bed as well as those of meltwater produced at the bed were calculated according to the gradient of the hydraulic potential. The inverted friction coefficients show the "unplugging" of the stagnant ice front and expansion of low-friction regions before the surge reached its peak velocity in January 2013. Crevasse distribution reflects the basal friction pattern to a high degree. The meltwater reaches the bed through the crevasses located above the margins of the subglacial valley and the basal melt that is generated mainly by frictional heating flows either to the fast-flowing units or potentially accumulates in an overdeepened region. Based on these results, the mechanisms facilitated by basal meltwater production, crevasse opening and the routing of meltwater to the bed are discussed for the surge in Basin 3.Peer reviewe

Modeling the elastic transmission of tidal stresses to great distances inland in channelized ice streams

Geodetic surveys suggest that ocean tides can modulate the motion of Antarctic ice streams, even at stations many tens of kilometers inland from the grounding line. These surveys suggest that ocean tidal stresses can perturb ice stream motion at distances about an order of magnitude farther inland than tidal flexure of the ice stream alone. Recent models exploring the role of tidal perturbations in basal shear stress are primarily one- or two-dimensional, with the impact of the ice stream margins either ignored or parameterized. Here, we use two- and three-dimensional finite-element modeling to investigate transmission of tidal stresses in ice streams and the impact of considering more realistic, three-dimensional ice stream geometries. Using Rutford Ice Stream as a real-world comparison, we demonstrate that the assumption that elastic tidal stresses in ice streams propagate large distances inland fails for channelized glaciers due to an intrinsic, exponential decay in the stress caused by resistance at the ice stream margins. This behavior is independent of basal conditions beneath the ice stream and cannot be fit to observations using either elastic or nonlinear viscoelastic rheologies without nearly complete decoupling of the ice stream from its lateral margins. Our results suggest that a mechanism external to the ice stream is necessary to explain the tidal modulation of stresses far upstream of the grounding line for narrow ice streams. We propose a hydrologic model based on time-dependent variability in till strength to explain transmission of tidal stresses inland of the grounding line. This conceptual model can reproduce observations from Rutford Ice Stream

7th Annual Jackson School of Geosciences Student Research Symposium, February 3, 2018

ConocoPhillipsGeological Science

Discrete element method simulation of packing and rheological properties of coke and coke/pitch mixtures

La production mondiale d’aluminium, produit via le procédé Hall Héroult, est actuellement autour de 60000 tonnes annuellement. Ce procédé a principalement conservé le concept original développé en 1886. Les anodes de carbone précuites utlisées dans ce procédé représentent une part importante du design des cellules d’électrolyse de l’aluminium. Les anodes font partie de la réaction chimique de la réduction de l’alumine et sont consommées lors du processus d’électrolyse. De ce fait, le niveau de consommation et la qualité des anodes ont un effet direct sur la performance des alumineries dans le marché extrêmement compétitif de la production d’aluminium. Bien que le processus et le design des anodes datent de 130 ans, l’effet des propriétés des matières premières sur la qualité finale des anodes n’est pas tout à fait maîtrisé, nécessitant ainsi des recherches approfondies. Les anodes de carbone sont composées de particules de coke, de pitch et de mégots d’anodes. Le pitch à la température de mélange et de formage est un liquide. Par conséquent, le mélange est une pâte de coke et des agrégats de mégots et pitch agissant comme liant. Le comportement de l'écoulement et du compactage de ce mélange en raison de la coexistence d'une variété de paramètres physiques, chimiques et mécaniques sont des phénomènes complexes. Compte tenu de l'importance des anodes de haute qualité et de longue durée en performance et donc l'économie des cellules de réduction, sous-estimer et prédire les propriétés finales des anodes sont très importantes pour les fonderies. La modélisation numérique dans des problèmes aussi complexes peut fournir un laboratoire virtuel où les effets de différents paramètres de processus ou des matériaux sur la qualité de l'anode peuvent être étudiés sans risquer la performance du pot. Toutefois, le choix de la méthode numérique est une décision critique qui doit être prise en fonction de la physique du problème et de l'échelle géométrique des problèmes étudiés. La méthode des éléments discrets (DEM) est utilisée dans ce travail de recherche pour modéliser les deux phases de la pâte d’anode; les agrégats de coke et le brai de pétrole. Dans cette partie du travail, les modèles DEM d’agrégats de coke sont utilisés pour simuler les tests de densité en vrac vibrée des particules de coke et pour révéler les paramètres impliqués. De par sa nature, la DEM est idéale pour étudier les contacts entre particules. Les résultats de ces travaux seront ensuite utilisés pour proposer de nouvelles recettes d’agrégats secs avec une densité en vrac supérieure. La résistivité électrique de lits de particules a été mesurée expérimentalement. Les informations sur les contacts entre particules obtenues à partir des modèles numériques ont été utilisées pour expliquer la résistivité électrique de lits de particules avec différentes distribution de tailles de particules. Les résultats ont montré que lorsque le nombre de contacts par unité de volume augmente dans un échantillon, la résistivité électrique augmente aussi. La densité compactée du lit de particules a aussi une influence sur le passage de courant dans les matériaux granulaires. D’après les résultats obtenus, conserver la densité de contacts aussi basse que possible est bénéfique pour la conductivité électrique s’il n’a pas d’impact négatif sur la densité compactée. Le brai de houille est un matériau viscoélastique à température élevée. Dans ce travail, les propriétés rhéologiques du brai et de la matrice liante (brai + particules fines de coke) ont été mesurées expérimentalement en utilisant un rhéomètre à cisaillement dynamique à 135, 140 145 et 150 °C. Le modèle de Burger à quatre éléments est alors utilisé pour modéliser le comportement mécanique du brai à 150 °C. Le modèle vérifié est alors utilisé pour étudier les propriétés rhéologiques du brai et du mélange coke /brai à 150 °C. Le modèle de Burger calibré démontre une bonne prédiction des propriétés viscoélastiques du brai et de la matrice liante à différentes températures. Les résultats obtenus montrent que, considérant la physique du problème, la méthode des éléments distincts est une technique de simulation numérique adaptée pour étudier les effets des matières premières sur les propriétés mécaniques et physiques des mélanges coke /brai.Global aluminum production now is around 60 000 metric tonnes, annually, which is produced by the Hall-Héroult process. The process has mostly kept the original concept developed in 1886. Pre-baked carbon anodes are an important part of the design of aluminum smelting cells. Anodes are part of the chemical reaction of alumina reduction and are consumed during the process. Thus, quality and properties of anodes have direct effects on the performance and economy of the aluminum production in today’s highly competitive market. Although the design of anodes goes back to 130 years ago, effects of raw materials properties on final quality of anodes still need to be investigated. Anodes are composed of granulated calcined coke, binder pitch and recycled anode butts. Pitch at temperatures of mixing and forming steps is a liquid. Hence the mixture is a paste of coke and butts aggregates with pitch acting as binder. Flow and compaction behavior of this mixture, because of the co-existence of a variety of physical, chemical and mechanical parameters are complicated phenomena. Given the importance of high quality and long lasting anodes in performance and so the economy of the reduction cells, understating and predicting the final properties of anodes are very important for smelters. Numerical modeling in such complicated problems can provide a virtual laboratory where effects of different materials or process parameters on anode quality index can be studied without risking the pot performance. However, the choice of the numerical framework is a critical decision which needs to be taken according to the physics of the problem and the geometrical scale of the investigated problems. Discrete Element Method (DEM) is used in this research work to model the anode paste. In the first step, DEM models of coke aggregates are used to simulate the vibrated bulk density test of coke particles and to reveal the parameters involved. As a micromechanical model, DEM provides a unique opportunity to investigate the particle-particle contacts. The developed DEM models of coke aggregates were then used to propose a new dry aggregates recipe exhibiting higher packing density. Packing density of coke aggregates has direct effect on the baked density of anodes. High density is a very favorable anode quality index as it has positive effects on mechanical strength, and consumption rate of anodes in the cell. Electrical resistivity of bed of particles was experimentally measured. Particle-particle contacts information obtained from numerical models were used to explain the electrical resistivity of samples with different size distribution. Results showed that the increase in the number of contacts in volume unit of a sample increases, the electrical resistivity of the particle bed. Packing density also influences the electrical current transfer in granular systems. According to the obtained results, keeping the contacts density as low as possible is beneficial for electrical conductivity if it does not have a negative effect on packing density. Pitch is a viscoelastic material at elevated temperatures. In the present work, rheological properties of pitch and binder matrix (pitch+fine coke particles) were experimentally measured using a dynamic shear rheometer at 135, 140, 145 and 150 ºC. Four-element Burger’s model is then used to model the mechanical behavior of pitch and binder matrix. The verified model is then used to investigate the rheological properties of pitch and coke/pitch mixtures at 150 ºC. Calibrated Burger’s model showed to have a good prediction of viscoelastic properties of pitch and binder matrix at different temperatures. Obtained numerical results showed that available empirical equations in the literature fail to predict the complex modulus of mixtures of pitch and coke particles. As pitch has viscoelastic response and coke particles have irregular shapes, rheology of this mixture is more complicated and needs well-tailored mathematical models. Complex modulus of pitch decreases by increasing the temperature from 135 to 150 ºC, this makes easier the coke/pitch mixtures to flow. DEM modeling showed that the mixture gets a better compaction and so lower porosity by vibro-compacting at higher temperatures. The ability of pitch to penetrate to inter-particle voids in the porous structure of bed of coke particles was also shown to be improved by temperature. Final anode structure with less porosity and so high density is favorable for its mechanical strength as well as its chemical reaction in the cell as Based on the obtained results and considering the physics of the problem, it can be said that discrete element method is an appropriate numerical simulation technique to study the effects of raw materials and the anode paste formulation on mechanical and physical properties of coke/pitch mixtures. The platform created in the course of this research effort, provides a unique opportunity to study a variety of parameters such as size distribution, shape and content of coke particles, content and rheological properties of pitch on densification of coke/pitch mixtures in vibro-compaction process. Outputs of this thesis provide a better understanding of complicated response of anode paste in the forming process

Development of a viscoelastic model of ice shelf dynamics

Climate Change has already caused large losses on natural occurring ice in the last decades and continues to do so. Antarctica, the largest source of land ice, contains an equivalent of several tens of meters of sea water level rise, which is induced not only by melting but also by out flow into ice shelves, the floating tongues of glaciers. In the last decades with recorded longer melt seasons and warming water in Antarctica, ice shelves are thinning and breaking up. With that, speed up of shelf inflowing glaciers are recorded, highlighting the buttressing force ice shelves have on glaciers and therefore their importance to the Antarctic Ice Sheet. Many factors play a role in the integrity of ice shelves, besides melting on the surface and from below, for example waves, tides and pressure imbalances at the calving front (buoyancy force) induce bending moments on short time scales. While ice is mainly studied as purely viscous, elastic or even plastic material. Certain ice shelf behaviour, like the tidal deformation near the grounding line or drainage of melt ponds, can only be sufficiently simulated with an viscoelastic model - representing the viscous thinning of ice as well as short term elastic bending deformations. Viscoelastic studies of ice so far have used commercial proprietary software, which require expensive licences and often lack inside in the used algorithms or flexibility to adapt the code as needed. In this thesis a viscoelastic model was developed in the open source FEM C++ environment Rheolef

A viscoelastic Rivlin-Ericksen material model applicable to glacier ice

We present a viscoelastic constitutive relation which describes transient creep of a modified second grade fluid enhanced with elastic properties of a solid. The material law describes a Rivlin-Ericksen material and is a generalization of existing material laws applied to study the viscoelastic properties of ice. The intention is to provide a formulation tailored to reproduce the viscoelastic behaviour of ice ranging from the instantaneous elastic response, to recoverable deformation, to viscous, stationary flow at the characteristic minimum creep rate associated with the deformation of polycrystalline ice. We numerically solve the problem of a slab of material shearing down a uniformly inclined plate. The equations are made dimensionless in a form in which elastic effects and/or the influence of higher order terms (i.e., strain accelerations) can be compared with viscous creep at the minimum creep rate by means of two dimensionless parameters. We discuss the resulting material behaviour and the features exhibited at different parameter combinations. Also, a viable range of the non-dimensional parameters is estimated in the scale analysis